https://drorbn.net/index.php?action=history&feed=atom&title=NCGE_Python_Code 2026-08-07T03:41:56Z Revision history for this page on the wiki MediaWiki 1.39.6 https://drorbn.net/index.php?title=NCGE_Python_Code&diff=10873&oldid=prev 2011-10-11T03:46:23Z

<p></p> <p><b>New page</b></p><div>class Perm(object):<br /> <br /> def __init__(self, L):<br /> if set(range(1,len(L) + 1)) == set(L):<br /> self.n = len(L)<br /> self.mapping = {}<br /> pivot_called = False<br /> for i in range(self.n):<br /> if not pivot_called:<br /> if L[i] != i+1:<br /> self.pivot = i+1<br /> pivot_called = True<br /> if not pivot_called:<br /> self.pivot = self.n<br /> self.mapping[i+1] = L[i]<br /> <br /> def __nonzero__(self):<br /> return self.pivot != self.n<br /> <br /> def __mul__(self,other):<br /> <br /> if self.n == other.n:<br /> L = []<br /> for i in range(1,self.n+1):<br /> L += [self.mapping[other.mapping[i]]]<br /> return Perm(L)<br /> <br /> def inv(self):<br /> <br /> L = []<br /> inverted = {}<br /> for i in range(1,self.n + 1):<br /> inverted[self.mapping[i]] = i<br /> for j in range(1,self.n + 1):<br /> L += [inverted[j]]<br /> return Perm(L)<br /> <br /> <br /> def e(n):<br /> <br /> return Perm(range(1,n+1))<br /> <br /> <br /> <br /> def gen_subgroup_order(L):<br /> <br /> homogenous_n = True<br /> perm1 = L[0]<br /> for perm in L:<br /> if perm.n != perm1.n:<br /> homogenous_n = False<br /> break<br /> <br /> if homogenous_n:<br /> X = L[:]<br /> n = perm1.n<br /> occupied = {}<br /> for k in range(1,n+1):<br /> occupied[(k,k)] = e(n)<br /> <br /> def feed(perm,Y,table):<br /> if bool(perm):<br /> i = perm.pivot<br /> j = perm.mapping[perm.pivot]<br /> <br /> if (i,j) not in occupied.keys():<br /> table[(i,j)] = perm<br /> <br /> else:<br /> sigma = table[(i,j)]<br /> Y += [(sigma.inv())*perm]<br /> <br /> for perm in X:<br /> feed(perm,X,occupied)<br /> <br /> old = 0<br /> new = len(occupied.keys())<br /> while old != new:<br /> X = []<br /> perms = occupied.values()<br /> for p1 in perms:<br /> for p2 in perms:<br /> if bool(p1) and bool(p2):<br /> X += [p1*p2]<br /> for perm in X:<br /> feed(perm,X,occupied)<br /> old, new = new, len(occupied.keys())<br /> <br /> order = 1<br /> for i in range(1,n+1):<br /> order *= len([pair for pair in occupied.keys() if pair[0] == i])<br /> return order<br /> <br /> g1 = Perm([1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32])<br /> <br /> g2 = Perm([1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32])<br /> <br /> g3 = Perm([14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17])<br /> <br /> g4 = Perm([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27])<br /> <br /> print gen_subgroup_order([g1,g2,g3,g4])</div>

Josh.seaton